I moved from VA to MA in 2024 and received income on a rental property located in VA while living in both states. How should I report that income on each state return?

The rental income is considered income from VA source. 

You need to report all rental income earned in 2024 on your VA part year return. Rental income earned after your moved to MA is also taxable on MA return. 

However, as a Massachusetts  part-year resident, you're allowed a credit for taxes due to another jurisdiction. The credit is available only on income reported and taxed on a Massachusetts return.

Massachusetts Department of Revenue

Thank you, and just so I'm clear, I should report all of the rental  income that I received on this VA rental property for the full year on my VA return and only the portion I received after moving to MA on my MA return, is that right?

Also, will TurboTax then automatically calculate and apply to my MA return a credit for the amount of tax that I paid on that rental income to VA or do I have to enter that credit amount somewhere in TurboTax for my MA return?

That is correct. 

For the credit, 

1. open MA return
2. Scroll down to Taxes and credits section
3. Continue to the screen Pay Tax To Another State?

For accurate calculation and to know the amount of VA tax you'll pay, complete VA return first.